The SEIQS stochastic epidemic model with external source of infection

This paper deals with a stochastic epidemic model for computer viruses with latent and quarantine periods, and two sources of infection: internal and external. All sojourn times are considered random variables which are assumed to be independent and exponentially distributed. For this model extinction and hazard times are analyzed, giving results for their Laplace transforms and moments. The transient behavior is considered by studying the number of times that computers are susceptible, exposed, infectious and quarantined during a period of time (0, t] and results for their joint and marginal distributions, moments and cross moments are presented. In order to give light this analysis, some numerical examples are showed.

Deep observation of the NGC1275 region with MAGIC: search of diffuse gamma-ray emission from cosmic rays in the Perseus cluster

Clusters of galaxies are expected to be reservoirs of cosmic rays (CRs) that should produce diffuse γ-ray emission due to their hadronic interactions with the intra-cluster medium. The nearby Perseus cool-core cluster, identified as the most promising target to search for such an emission, has been observed with the MAGIC telescopes at very-high energies (VHE, E ≥ 100 GeV) for a total of 253 hr from 2009 to 2014. The active nuclei of NGC 1275, the central dominant galaxy of the cluster, and IC 310, lying at about 0.6º from the centre, have been detected as point-like VHE γ-ray emitters during the first phase of this campaign. We report an updated measurement of the NGC 1275 spectrum, which is described well by a power law with a photon index Γ = 3.6 ± 0.2_(stat) ± 0.2_(syst) between 90 GeV and 1200 GeV. We do not detect any diffuse γ-ray emission from the cluster and so set stringent constraints on its CR population. To bracket the uncertainties over the CR spatial and spectral distributions, we adopt different spatial templates and power-law spectral indexes α. For α = 2.2, the CR-to-thermal pressure within the cluster virial radius is constrained to be ≤ 1 − 2%, except if CRs can propagate out of the cluster core, generating a flatter radial distribution and releasing the CR-to-thermal pressure constraint to ≤ 20%. Assuming that the observed radio mini-halo of Perseus is generated by secondary electrons from CR hadronic interactions, we can derive lower limits on the central magnetic field, B_(0), that depend on the CR distribution. For α = 2.2, B_(0) ≥ 5 − 8 µG, which is below the ∼25 µG inferred from Faraday rotation measurements, whereas for α ≤ 2.1, the hadronic interpretation of the diffuse radio emission contrasts with our γ-ray flux upper limits independently of the magnetic field strength.

Low-resolution spectroscopy and spectral energy distributions of selected sources towards σ Orionis

Aims. We study in detail nine sources in the direction of the young σ Orionis cluster, which is considered to be a unique site for studying stellar and substellar formation. The nine sources were selected because of their peculiar properties, such as extremely-red infrared colours or excessively strong Hα emission for their blue optical colours. Methods. We acquired high-quality, low-resolution spectroscopy (R ∼ 500) of the nine targets with ALFOSC at the Nordic Optical Telescope. We also re-analysed [24]-band photometry from MIPS/Spitzer and compiled the highest quality photometric dataset available at the ViJHK_s passbands and the four IRAC/Spitzer channels, for constructing accurate spectral energy distributions between 0.55 and 24 μm. Results. The nine targets were classified into: one Herbig Ae/Be star with a scattering edge-on disc; two G-type stars; one X-ray flaring, early-M, young star with chromospheric Hα emission; one very low-mass, accreting, young spectroscopic binary; two young objects at the brown-dwarf boundary with the characteristics of classical T Tauri stars; and two emission-line galaxies, one undergoing star formation, and another whose spectral energy distribution is dominated by an active galactic nucleus. We also discovered three infrared sources associated with overdensities in a cold cloud of the cluster centre. Conclusions. Low-resolution spectroscopy and spectral energy distributions are a vital tool for measuring the physical properties and evolution of young stars and candidates in the σ Orionis cluster.